An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. If two marbles are picked up at random, what is the probability that either both are green or both are yellow ?

Answer: Option D

Total number of marbles = (6 + 4 + 2 + 3) = 15
Let E be the event of drawing 2 marbles such that either both are green or both are yellow.
Then,
n (E) = $$\left({}^2{C}_1+{}^3{C}_2\right)$$   $$=\left(1+{}^3{C}_1\right)$$   = (1 + 3) = 4
And, n (S) = $${}^{15}{C}_2=$$   $$\frac{15\times 14}{2\times 1}$$   = 105
$$\therefore P(E)=\frac{n(E)}{n(S)}=\frac{4}{105}$$